Let (a_{n} ; n\ge 1),
(b_{n}; n\ge 1) and
(l_{n}; n\ge 1)
be three sequences of real numbers. Supose that
l_{n} \in [0,1]
for every n, and let
c_{n}=l_{n}a_{n}+(1-l_{n})b_{n}.
Assuming that
lim sup a_{n} and
lim sup b_{n} are finite, please
prove the following inequality:

lim sup c_{n} \le max(lim sup a_{n},lim sup b_{n})